Theorems · Inductive type · logic and foundations
Cardinal.IsStrongLimit
Cardinal.{u_1} → PropA cardinal is a strong limit if it is not zero and it is closed under powersets.
Note that ℵ₀ is a strong limit by this definition.
See IsStrongPrelimit for a version including 0.
- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
Cited by18
Results whose statement or proof uses this declaration.
- Cardinal.IsStrongLimit.isStrongPrelimitstatement and proof · cited by 4
- Cardinal.IsStrongLimit.isSuccLimitstatement and proof · cited by 3
- Cardinal.IsStrongLimit.aleph0_lestatement and proof · cited by 2
- Cardinal.IsStrongLimit.ne_zerostatement and proof · cited by 2
- Cardinal.IsInaccessible.isStrongLimitstatement · cited by 2
- Cardinal.IsStrongLimit.casesOnstatement and proof · cited by 1
- Cardinal.IsStrongLimit.univstatement · cited by 1
- Cardinal.isStrongLimit_iffstatement and proof · cited by 1
- Cardinal.isStrongLimit_preBethstatement · cited by 1
- Cardinal.mk_bounded_subsetproof · cited by 1
- Cardinal.isInaccessible_defstatement and proof · cited by 0
- Cardinal.IsStrongLimit.isSuccPrelimitstatement and proof · cited by 0